An adaptive and nonlinear drift-based Wiener process for remaining useful life estimation

Remaining useful life (RUL) is considered as the one of most central components in prognostics and health management. In this paper, we present an adaptive and nonlinear drift-based diffusion process for RUL estimation. Specifically, we first adopt a Wiener process with a nonlinear and time-dependent drift coefficient to characterize the dynamics and nonlinearity of the degradation process. In order to make the RUL estimation depending on the history of the observations, we construct a state space model to updating one parameter in the drifting function through Bayesian filtering. The probability density function of the RUL is derived as well. To update the hidden state (e.g. drifting parameter) and other parameters in the state space model simultaneously and recursively, the expectation maximization algorithm can be used in conjunction with Kalman filter to achieve this aim. We demonstrate the proposed method with a numerical example. The results indicate that our method can generate better results than the linear models.